Group #18069624 — subgroups

Subgroups — #18069624

Order 4864.

286 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563673	C₂	1	1	yes	maximal, characteristic
2	#14563664	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2112	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	1	no	—
5	C₂×#10597275	—	2	1	no	—
6	#11926508	—	2	1	no	—
7	#11926404	—	2	1	no	—
8	#11926309	C₄	1	2	yes	complemented
9	#11926307	C₄	1	2	yes	—
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×M₃₂	C₄	1	2	yes	complemented
12	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
13	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
14	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	—	4	2	no	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₂²⋊Dic₁₉	—	4	1	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×#64520	—	2	2	no	—
25	C₁₉×M₃₂	—	4	2	no	—
26	C₂×C₁₆×C₁₉	—	2	2	no	—
27	C₁₉⋊#95	—	4	1	no	—
28	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
30	#10597276	—	4	2	no	—
31	#10597275	—	4	2	no	—
32	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	—	4	1	no	—
34	C₂²×C₄×C₁₉	—	4	1	no	—
35	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
41	C₂²×Dic₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	2	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	4	1	no	—
46	C₂×C₈×C₁₉	—	4	1	no	—
47	C₂×C₈×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂²⋊Dic₁₉	—	8	2	no	—
53	C₄⋊Dic₁₉	—	4	2	no	—
54	C₄⋊Dic₁₉	—	4	2	no	—
55	#64520	—	4	2	no	—
56	#64520	—	4	2	no	—
57	C₂×C₁₉⋊C₈	—	4	2	no	—
58	C₁₆×C₁₉	—	4	2	no	—
59	#7235	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	—	2	1	no	—
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	4	1	no	—
63	C₂³×C₁₉	—	4	1	no	—
64	C₂³×C₁₉	#102	1	1	yes	characteristic
65	C₂³×C₁₉	#103	1	1	yes	characteristic
66	C₂³×C₁₉	#106	1	1	yes	characteristic
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	4	1	no	—
74	C₂×C₄×C₁₉	—	4	1	no	—
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
80	C₂×Dic₁₉	—	8	2	no	—
81	C₂×Dic₁₉	—	8	2	no	—
82	C₂×Dic₁₉	—	8	2	no	—
83	C₈×C₁₉	—	2	1	no	—
84	C₈×C₁₉	—	2	1	no	—
85	C₈×C₁₉	—	2	1	no	—
86	C₈×C₁₉	#99	1	2	yes	—
87	C₁₉⋊C₈	—	8	2	no	—
88	#2112	D₁₉	1	1	yes	characteristic
89	#1810	—	19	1	no	—
90	#1808	—	19	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	—	2	1	no	—
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	2	1	no	—
95	C₂²×C₁₉	—	2	1	no	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	—	4	2	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	#340	1	1	yes	characteristic
102	C₂²×C₁₉	#361	1	1	yes	characteristic
103	C₂²×C₁₉	#362	1	1	yes	characteristic
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
108	C₄×C₁₉	#342	1	1	yes	characteristic
109	Dic₁₉	—	16	2	no	—
110	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×M₃₂	Dic₁₉	1	2	yes	complemented
112	C₂×#108	—	38	1	no	—
113	C₂×#107	—	38	1	no	—
114	#407	—	38	1	no	—
115	#380	—	38	1	no	—
116	C₂²⋊C₁₆	—	2	1	no	—
117	C₂²⋊C₁₆	—	2	1	no	—
118	#341	—	19	2	no	—
119	#340	—	19	2	no	—
120	C₂×C₁₉	—	2	1	no	—
121	C₂×C₁₉	—	2	1	no	—
122	C₂×C₁₉	—	4	1	no	—
123	C₂×C₁₉	—	4	1	no	—
124	C₂×C₁₉	#1289	1	1	yes	characteristic
125	C₂×C₁₉	#1387	1	1	yes	characteristic
126	C₂×C₁₉	#1389	1	1	yes	characteristic
127	C₂³×C₄	D₇₆	1	1	yes	characteristic
128	C₂×M₁₆	—	38	2	no	—
129	C₂²×C₈	—	4	2	no	—
130	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
131	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
132	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
133	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
135	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
136	C₂×C₄⋊C₄	—	38	2	no	—
137	C₂×C₂²⋊C₄	—	76	1	no	—
138	M₃₂	—	4	2	no	—
139	C₂×C₁₆	—	2	2	no	—
140	#108	—	76	2	no	—
141	#107	—	76	2	no	—
142	C₂²⋊C₈	—	76	1	no	—
143	C₂²⋊C₈	—	76	1	no	—
144	#95	—	76	1	no	—
145	C₁₉	#7235	1	1	yes	characteristic, complemented, Sylow
146	C₂⁴	#64516	1	1	yes	characteristic
147	C₂²×C₄	—	4	1	no	—
148	C₂²×C₄	—	4	1	no	—
149	C₂²×C₄	—	76	2	no	—
150	C₂²×C₄	#64516	1	1	yes	characteristic
151	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
152	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
153	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
154	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
155	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
156	M₁₆	—	76	2	no	—
157	M₁₆	—	76	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	4	1	no	—
162	C₂×C₈	—	4	1	no	—
163	C₂×C₈	—	4	1	no	—
164	C₂×C₈	—	76	2	no	—
165	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
166	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
167	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
168	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
169	C₄⋊C₄	—	76	2	no	—
170	C₄⋊C₄	—	76	2	no	—
171	C₂²⋊C₄	—	152	2	no	—
172	C₁₆	—	4	2	no	—
173	C₂³	—	2	1	no	—
174	C₂³	—	2	1	no	—
175	C₂³	—	4	1	no	—
176	C₂³	—	4	1	no	—
177	C₂³	#10597273	1	1	yes	characteristic
178	C₂³	#10597274	1	1	yes	characteristic
179	C₂³	#10597278	1	1	yes	characteristic
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	152	2	no	—
190	C₂×C₄	—	152	2	no	—
191	C₂×C₄	—	152	2	no	—
192	C₂×C₄	#10597273	1	1	yes	characteristic
193	C₂×C₄	#10597275	1	1	yes	characteristic
194	C₂×C₄	#10597278	1	1	yes	characteristic
195	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	2	1	no	—
199	C₈	—	152	2	no	—
200	C₈	#10597291	1	2	yes	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	2	1	no	—
205	C₂²	—	2	1	no	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	4	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	#11926307	1	1	yes	characteristic
212	C₂²	#11926358	1	1	yes	characteristic
213	C₂²	#11926361	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	304	2	no	—
218	C₄	#11926301	1	1	yes	characteristic
219	C₄	#11926311	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	—	4	1	no	—
223	C₂	—	4	1	no	—
224	C₂	#14561503	1	1	yes	characteristic
225	C₂	#14561744	1	1	yes	characteristic
226	C₂	#14561750	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563673

C₂

yes

maximal, characteristic

#14563664

C₂

yes

maximal, characteristic

C₁₉×#2112

C₂

yes

maximal, characteristic

—

—

—

—

C₄

yes

complemented

#11926307

C₄

yes

—

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×M₃₂

C₄

yes

complemented

C₁₉×C₂²⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

#10597275

—

C₂⁴×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

#7235

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#99

yes

—

C₁₉⋊C₈

—

#2112

D₁₉

yes

characteristic

#1810

—

#1808

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

#340

yes

characteristic

102

C₂²×C₁₉

#361

yes

characteristic

103

C₂²×C₁₉

#362

yes

characteristic

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

H(3,ℤ/4)

yes

characteristic

108

C₄×C₁₉

#342

yes

characteristic

109

Dic₁₉

—

110

C₂³×C₈

C₂×D₁₉

yes

characteristic

111

C₂×M₃₂

Dic₁₉

yes

complemented

112

C₂×#108

—

113

C₂×#107

—

114

#407

—

115

#380

—

116

C₂²⋊C₁₆

—

117

C₂²⋊C₁₆

—

118

#341

—

119

#340

—

120

C₂×C₁₉

—

121

C₂×C₁₉

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#1289

yes

characteristic

125

C₂×C₁₉

#1387

yes

characteristic

126

C₂×C₁₉

#1389

yes

characteristic

127

C₂³×C₄

D₇₆

yes

characteristic

128

C₂×M₁₆

—

129

C₂²×C₈

—

130

C₂²×C₈

Dic₃₈

yes

characteristic

131

C₂²×C₈

C₄×D₁₉

yes

characteristic

132

C₂²×C₈

C₄×D₁₉

yes

characteristic

133

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

134

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

135

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

136

C₂×C₄⋊C₄

—

137

C₂×C₂²⋊C₄

—

138

M₃₂

—

139

C₂×C₁₆

—

140

#108

—

141

#107

—

142

C₂²⋊C₈

—

143

C₂²⋊C₈

—

144

#95

—

145

C₁₉

#7235

yes

characteristic, complemented, Sylow

146

C₂⁴

#64516

yes

characteristic

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

#64516

yes

characteristic

151

C₂²×C₄

D₁₅₂

yes

characteristic

152

C₂²×C₄

Dic₇₆

yes

characteristic

153

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

154

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

155

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

156

M₁₆

—

157

M₁₆

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

C₄×Dic₁₉

yes

characteristic

166

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

167

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

168

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₂²⋊C₄

—

152

—

172

C₁₆

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

#10597273

yes

characteristic

178

C₂³

#10597274

yes

characteristic

179

C₂³

#10597278

yes

characteristic

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

152

—

190

C₂×C₄

—

152

—

191

C₂×C₄

—

152

—

192

C₂×C₄

#10597273

yes

characteristic

193

C₂×C₄

#10597275

yes

characteristic

194

C₂×C₄

#10597278

yes

characteristic

195

C₂×C₄

C₁₉⋊#95

yes

characteristic

196

C₈

—

197

C₈

—

198

C₈

—

199

C₈

—

152

—

200

C₈

#10597291

yes

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

#11926307

yes

characteristic

212

C₂²

#11926358

yes

characteristic

213

C₂²

#11926361

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

304

—

218

C₄

#11926301

yes

characteristic

219

C₄

#11926311

yes

characteristic

220

C₂

—

221

C₂

—

222

C₂

—

223

C₂

—

224

C₂

#14561503

yes

characteristic

225

C₂

#14561744

yes

characteristic

226

C₂

#14561750

yes

characteristic

	subgroup	G/H
center	C₂²	#11926307
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂³×C₈	C₂×D₁₉
Fitting	C₁₉×#2112	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂⁴×C₁₉	SD₁₆
cosocle	C₂³×C₈×C₁₉	C₂²
hypercenter	#2112	D₁₉
hypocenter	C₁₉	#7235
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂²

#11926307

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂³×C₈

C₂×D₁₉

Fitting

C₁₉×#2112

C₂

socle

C₂²×C₁₉

#340

prime radical

C₂⁴×C₁₉

SD₁₆

cosocle

C₂³×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
8. #11926309	C₄	semidirect
11. C₂×C₁₉×M₃₂	C₄	semidirect
111. C₂×M₃₂	Dic₁₉	semidirect
145. C₁₉	#7235	semidirect

H ≅ G/N

type

8. #11926309

C₄

semidirect

11. C₂×C₁₉×M₃₂

C₄

semidirect

111. C₂×M₃₂

Dic₁₉

semidirect

145. C₁₉

#7235

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14563673	2
#14563664	2
C₁₉×#2112	2
#7235	19

subgroup

index

#14563673

#14563664

C₁₉×#2112

#7235

Subgroups — #18069624

Conjugacy classes of subgroups

Complements

Maximal subgroups